Matlab Final Theory Questions

Euler's method is usually more accurate than Heun's method for the same step size.

False

The Composite Simpson's 1/3 Rule can be used to obtain the integral over an interval divided into n=5 segments. End Quiz 3

False

A system of equations can be written in the form: Ax=b, where A is a square matrix, x is a vector of unknowns, and b is a vector of constants. End Exam 2

True

Adaptive Quadrature adjusts to use a smaller step size in areas where the function changes rapidly, and a larger step size where the function changes slowly.

True

Quadrature is another name for integration.

True

Start Quiz 6 If λ 1 is an eigenvalue associated with eigenvector ν 1, then A ν 1 = λ 1 ν 1.

True

The main disadvantage of the Newton-Raphson method is that it may not converge. (T/F)

True

Start Quiz 3 Simpson's 1/3 Rule can be used to calculate the integral of a function or data with unequal-width segments.

False

Given a system of equations Ax=b, if det(A)≠0 and the number of equations equals the number of unknowns, there is a unique solution. End Quiz 4

True

In general, the Composite Trapezoid Rule is more accurate than a single application of the Trapezoid Rule.

True

The determinant of a matrix is a scalar.

True

Which of the following conditions are boundary value problems?

Can be y or y' values, just as to be at the end points

There are three "types" of numerical derivative approximations: forward, backward, and centered. End Quiz 6

True

Vectors are transposed using the single quote operator. (T/F)

True

If the function values of a bracket have the same sign, there are guaranteed to be no roots in the bracket. (T/F)

False

Implicit Euler's method is only conditionally stable. end Quiz 5

False

Partial differential equations have a single independent variable.

False

The Composite Simpson's 3/8 Rule can be used to obtain the integral over an interval divided into n=5 segments.

False

The key to Gauss Quadrature is to balance the function values.

False

The main advantage of the modified secant method is that it does not require specifying a value for Δ x. (T/F) Quiz 2 End

False

The numerical approximations of the derivatives discussed in class were derived from Newton-Raphson theory.

False

The only way to increase the accuracy of a numerical approximation of a derivative is to add more terms in the Taylor Series used to derive the approximation.

False

The Trapezoidal Rule approximates the function by a straight line

Straight Line

Eigenvalues indicate how fast a stable mode decays since the response can be written as: x ( t ) = C e ^(λ t).

True

For non-linear ODEs, we can use the shooting method along with a root finding method to drive the error in the given boundary condition to zero.

True

Gauss Elimination is the systematic process of removing unknowns using forward elimination followed by back substitution to obtain the unknown values.

True

Initial value problems have all necessary conditions given at a single value of the independent variable.

True

Missing Quiz 1 Start Quiz 2 The main disadvantage of the false position method is that it is one-sided. (T/F)

True

Naïve Gauss elimination can fail due to division by zero.

True

Romberg's method can be used to combine two O(h2) estimates of the integral to obtain a single O(h4) estimate.

True

The Newton-Raphson method is based on determining the intersection of the tangent of the function and the x-axis. (T/F)

True

The fourth order Runge-Kutta method is based on calculating the final slope, phi, where phi is a weighted average of four slopes. True

True

The key to Gauss Quadrature is to balance the positive and negative errors.

True

The main advantage of the bisection algorithm is that it always converges. (T/F)

True

The method of elimination involves eliminating unknowns by combining equations.

True

How many times will the following function display "hello" if z is inputted to be 3?

see photo (not 1)

Which command will generate a surface plot with contours?

surfc

Discontinous functions can result in a bracket with opposite-signed function values having an even number of roots. (T/F)

true

One disadvantage of the Newton-Raphson method is that it requires the user to analytically find the derivative of the function. (T/F)

true

The roots of a function f(x) are located at the points where the function crosses the x-axis. (T/F)

true

An iterative technique is used to find an approximate solution. The true solution is 5.80. The table below shows the approximate solution by iteration number. What is the percent relative approximate error for the second iteration? Iteration 1 2 3 4 5 Approximation 8.78 7.42 6.84 6.48 6.21 End Exam 1 questions

-18.3288

Given that: g = 5, h = 4 and k = 8 Evaluate D 3 = D 2 − D 1, where D 1 = 42 π /h and D 2 = sqrt(g ⋅ k) + h. Input your answer to 4 decimal places.

-22.6626

A single application of Simpson's 1/3 Rule requires computing the value of the function at how many points?

3

Which of the following are types of boundary conditions we discussed in class?

Dirichet Neumann Robin

Adaptive Quadrature uses more segments in regions where the function changes slowly.

False

Start Quiz 4 Which of the following techniques has the primary benefit of being more efficient when having to calculate the solution to a system of equations Ax = b with multiple b vectors?

LU Factorization

Which of the following techniques has the primary benefit of being more efficient when having to calculate the solution to a system of equations Ax = b with multiple b vectors?

LU Factorization

Start Quiz 5 Which of the following are caused by the finite precision of a computer?

Round off Errors

Exam 2 Start Romberg's Integration involves multiple applications of which rule?

Trapezoid

A TA is creating the following function header, but can't remember how to specify an output. Click the dropdown menu and select the correct component. function [grade] = autoGrader(aNumber, answersArray)

[grade]=

For the bisection algorithm, the number of iterations required to attain a particular error cannot be calculated in advance. (T/F)

false

The main advantage of the secant method is that it is guaranteed to converge. (T/F

false

The main disadvantage of the false position method is that it can diverge. (T/F)

false

Which one of the following functions can be used to find the number of roots of a function between a specified lower and upper bound?

incsearch (probably)